Related papers: Atomistic-Continuum Coupling by Homogenization

The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a two-level atom and an ensemble of two-level atoms both…

Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…

The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by…

Molecular dynamics simulations demand an unprecedented combination of accuracy and scalability to tackle grand challenges in catalysis and materials design. To bridge this gap, we present AlphaNet, a local-frame-based equivariant model that…

We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact…

Ab initio simulations of dislocations are essential to build quantitative models of material strength, but the required system sizes are often at or beyond the limit of existing methods. Many important structures are thus missing in the…

Molecular dynamics simulations are used to study different definitions of contact at the atomic scale. The roles of temperature, adhesive interactions and atomic structure are studied for simple geometries. An elastic, crystalline substrate…

Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…

Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element…

It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is introduced to describe the dynamics of a system…

The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian…

This study proposes a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures. The effect of the microstructural heterogeneity is taken into account by means of periodic…

Homogeneous nucleation processes are important for understanding solidification and the resulting microstructure of materials. Simulating this process requires accurately describing the interactions between atoms, hich is further…

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact.…

A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads…

Our exact theory for continuous harmonic perturbation of a one dimensional model atom by parametric variations of its potential is generalized for the cases when a) the atom is exposed to short pulses of an external harmonic electric field…

A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…

Many thermodynamic instabilities in one dimension (e.g. DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential…

Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global…

The accurate computational determination of chemical, materials, biological, and atmospheric properties has critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of…